A preliminary simulative assessment of disproportionality indices

What do indices of disproportionality actually measure? They provide an aggregate estimation of the difference between votes cast and seats assignment, but the relation between the value of the indices and the will of the voters is highly questionable. The reason is that when casting the vote the voter is deeply affected by the electoral system itself, possibly more deeply than s/he understands. The aim of this paper is to assess the performance of the most used indices of disproportionality with respect to the will of voters. To do so we compare by simulation their performance in some major electoral systems and with reference to some stylised typical cases. We use as a benchmark a "true" index, i.e. an index that measures the difference between the will of the voters (instead of the votes) and the assignment of seats. In our experiment all the indices considered perform poorly, with the unexpected exception of the Loosemore-Hanby index.